I really like the method the Grey Seal Puppets' "The Foam Book" describes. (
http://www.greysealpuppets.com/) Fundamentally it is an axle made from a doll joint and a wire arm rod bent into a hook that locks into it. The doll joint is embedded nto the palm area of the puppet's hand. It is very firm, articulates during performance, and doesn't come out unless I want it to.
Of course there are hundreds of ways to go about it. I've seen people use threaded rods into clevises from RC kits, magnetics, etc. etc., but the Grey Seal way has worked really well for me. I highly recommend their book!